Abstract

In this thesis I report on experiments that enter a new regime in
the many body physics of ultracold atomic gases. A Bose-Einstein
condensate is loaded into a three-dimensional optical lattice
potential formed by a standing wave laser light field. In this
novel quantum system we have been able to both realize a quantum
phase transition from a superfluid to a Mott insulator, and to
observe the collapse and revival of a macroscopic matter wave
field.
Quantum phase transitions are driven by quantum fluctuations and
occur, even at zero temperature, as the relative strength of two
competing energy terms in the underlying Hamiltonian is varied
across a critical value. In the first part of this work I report
on the observation of such a quantum phase transition in a
Bose-Einstein condensate with repulsive interactions, held in a
three-dimensional optical lattice potential. In the superfluid
ground state, each atom is spread-out over the entire lattice,
whereas in the Mott insulating state, exact numbers of atoms are
localized at individual lattice sites. We observed the reversible
transition between those states and detected the gap in the
excitation spectrum of the Mott insulator.
A Bose-Einstein condensate is usually described by a macroscopic
matter wave field. However, a quantized field underlies such a
"classical" matter wave field of a Bose-Einstein condensate. The
striking behavior of ultracold matter due to the field
quantization and the nonlinear interactions between the atoms is
the focus of the second part of this work. The matter wave field
of a Bose-Einstein condensate is observed to undergo a series of
collapses and revivals as time evolves. Furthermore, we show that
the collisions between individual pairs of atoms lead to a fully
coherent collisional phase shift in the corresponding
many-particle state, which is a crucial cornerstone of proposed
novel quantum computation schemes with neutral atoms.
With these experiments we enter a new field of physics with
ultracold quantum gases. In this strongly correlated regime,
interactions between atoms dominate the behavior of the many-body
system such that it can no longer be described by the usual
theories for weakly interacting Bose gases. This novel quantum
system offers the unique possibility to experimentally address
fundamental questions of modern solid state physics, atomic
physics, quantum optics, and quantum information.